Cross-Spectrum FFT Analysis
The program Cross narrow-band spectrum is used for evaluation of the interrelation of the signals’ parameters obtained from the two primary transducers installed at various parts of the controlled object. This program can be used for detection of noise source location, for sound absorption level evaluation and the researched object acoustic properties control, for evaluation of space-time distribution of the directional energy flux (Umov-Poynting vector), for the ground cross-section FR characteristic evaluation (Nakamura method), etc.
The program Cross narrow-band spectrum is used for calculation of power cross-spectrum, phase spectra, coherence spectra, pulse-response characteristics, as well as for resonance calculation.
Cross narrow-band spectrum program enables graphical representation of various spectral characteristics of the signals, thus, allowing to reveal the enhanced vibration amplitudes at resonance frequencies of the researched object or the components of a complex system. These functions allow to timely reveal the defects and to undertake corresponding preventive measures.
Implementation of the cross narrow-band spectrum analysis of the signals received from the input channels of the FFT Spectrum analyzers is possible both in the real-time mode and the accumulated data post-processing mode.
Cross narrow-band spectrum belongs to the group of classical signal analysis methods and is widely applicable for almost all classes of signals having stationary properties.
Main functions of the program
- measurement and representation of the signal in narrow spectral bands. The number of bands can be equal to the power of two (128, 256, 512, …, 262144) or to an arbitrary number (e.g., 100, 200, 500, …, 250000) with the use of Z-conversion;
- measurement and representation of signal spectral characteristics with various averaging types (linear, exponential), processing (integration, differentiation) and representation (RMS or peak value);
- measurement and representation of real and imaginary part of the signal, phase difference and signals coherence coefficient;
- measurement and displaying of the instant spectrum modulus;
- measurement of the complex frequency response and coherent power of the spectral component;
- measurement and graphical representation of signals transfer characteristics.
The software allows to use additional dialog windows with a graphical representation of the following parameters:
- Real part – representation of the source signal co-phase component amplitude;
- Imaginary part – representation of the source signal two-phase component;
- Phase – joint representation of the signal source components;
- Coefficient of coherence – representation of phase synchronization of the two signals;
- Transient characteristic – representation of the controlled object response to a single stepwise impact;
- Impulse characteristic – representation of the controlled object response to a single pulse impact;
- Impulse characteristic (coherent) – representation of the controlled object response to a single pulse impact taking into consideration the phase synchronization of the signals;
- Nyquist diagram – representation of amplitude-frequency response (AFR);
- Calculation of resonances – search and representation of the controlled object natural oscillations.
The figure below shows an additional window “Calculation of resonances” of the program “Cross narrow-band spectrum“. The “Calculation of resonances” enables analysis of frequency response characteristics of the physical systems exposed to a certain pulse impact.
The dialog window is separated into 5 sections used for the real-time representation of the controlled parameters values. The upper section of the window contains graphical representation of the signal phase, a log with the resonance frequencies and the corresponding parameters (natural oscillations, resonance frequency, Q-factor, damping ratio and amplitude). The bottom part of the window is used for constant recording and representation of the parameter selected by the user (it is also possible to select several parameters), that are related to the resonance frequency. This section of the program interface is also used for the control of the researched parameter’s dynamics. The parameters to be displayed are selected with a corresponding checkbox. The following parameters are available for the graphical representation: natural oscillations (Fnat.), resonance frequency (Fres.), Q-factor (Q), damping ratio (β), phase and amplitude.
Specialists of ZETLAB Company have reproduced one of the first laboratory experiments aimed at evaluation of the frequency response characteristics in one – dimensional systems. A similar experiment has been conducted by Barnoski in the following way: a beam is attached to the vibration exciter mounting in such a way so that one end of the beam would be firmly fixed to the center of the vibration exciter fixture while the other is in a free position. Frequency response characteristics control is conducted by means of two accelerometers – one is placed at the vibration exciter (to register the input impact), while the other one is mounted at the free end of the beam (to register the output signal). The input impact is represented by the broad-band random vibration produced by the shaker controller (VCS) ZET 017-U (hereinafter referred to as VCS ZET 017-U).
The evaluation of amplitude and phase characteristic is shown in the graphs at the top section of the program interface. As you can see, the amplitude characteristic has a clear peak at the frequency of ∼ 56 Hz, while the phase characteristic changes drastically at the same very frequency level (such graphs are quite typical for the systems with a single degree of freedom). These factors clearly reveal the first normal mode of the beam which is to be controlled.
In spite of the fact that accurate evaluation of the frequency response characteristic implies adherence to the system linearity requirements (while the linearity is a rare system property in real conditions), the cross narrow-band spectrum analysis allows to obtain comprehensive results, that describe the best possible (RMS) linear approximations of the researched systems. This is especially important when it comes to extremum values statistics research for the prevention of buildings and structures destruction caused by accidental impact. [J. Bendat, A. Piersol: “Engineering Applications of Correlation and Spectral Analysis”, 1983].
Cross-spectral densities are represented as functions with frequency dependence. This fact allows to use the spectral analysis in the engineering tasks domain (where previously the correlational methods used to be widely spread).
An important advantage of the cross narrow-band spectrum (if compared to the correlation analysis) is that it is unnecessary to have a dispersion-free environment.
Cross narrow-band spectrum analysis is also used for localization of the signal source.
The spectral density parameter is a convenient tool for direct evaluation of physical systems properties based on input and output parameters of the system (the same principle is applicable to multi-dimensional systems).